Logical Credal Networks
This work addresses the challenge of integrating logic and probability for applications like game-solving and fraud detection, offering a novel framework that is more expressive than previous models.
The paper tackles the problem of combining logic and probability under imprecise information by introducing Logical Credal Networks, a probabilistic logic that generalizes prior models and allows flexible propositional and first-order logic formulas. The results show it outperforms existing approaches in maximum a posteriori inference tasks, such as solving Mastermind games with uncertainty and detecting credit card fraud, by effectively aggregating multiple sources of imprecise information.
This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional probability bounds of logic formulas, this logic specifies a set of probability distributions over all interpretations. On the one hand, our approach allows propositional and first-order logic formulas with few restrictions, e.g., without requiring acyclicity. On the other hand, it has a Markov condition similar to Bayesian networks and Markov random fields that is critical in real-world applications. Having both these properties makes this logic unique, and we investigate its performance on maximum a posteriori inference tasks, including solving Mastermind games with uncertainty and detecting credit card fraud. The results show that the proposed method outperforms existing approaches, and its advantage lies in aggregating multiple sources of imprecise information.